Labour peer Lord Levy, a former chief fundraiser for the party, said he was considering his membership following the decision to not expel Ken Livingstone.
He told BBC Radio 4’s Today programme: “I’m very upset with the party’s attitude, I do not believe there has been a zero tolerance policy towards anti-Semitism.
“But once you’ve made a decision to leave the party, you’ve made it, and shouting from outside does not have the impact as staying in and making changes from within.”
He went on to call Jeremy Corbyn “a failed leader who is not leading our party forward as a serious opposition party”.
The decision to suspend Livingstone from the party for a further year rather than expel him was branded “pathetic” by Labour MP John Woodcock.
He tweeted: “This pathetic Livingstone sentence is an important moment Labour members: do we stand for decency against this or are we part of the decay?”
The MP also attacked Labour’s shadow attorney general, Shami Chakrabarti’s stance on the issue, adding: “There is no third way. Baroness Chakrabarti’s defence of this appalling decision just gives the impression that our party has lost its way.”
Labour MP Wes Streeting tweeted: “So much for zero tolerance approach to anti-Semitism – this is a terrible betrayal of Jewish Labour supporters and our values.”
Holocaust Educational Trust chief executive officer Karen Pollock said: “This verdict is a slap on the wrist for a serial offender. That a mainstream political party would consider these views to be welcome within their ranks simply demonstrates that anti-Semitism is not taken as seriously as all other forms of racism and prejudice.”
Jewish Leadership Council chief executive Simon Johnson said: “Given that Ken Livingstone has been found guilty, we are deeply disappointed at the decision not to expel him from the Labour Party. A temporary suspension is no more than a slap on the wrist.
“We feel that the Labour Party should have had the courage to address this deeply offensive behaviour with a firmer penalty.”
Joe Glasman, of the Campaign Against Anti-Semitism, said: “Ken Livingstone has been portraying Jews as Nazis for decades. His claim that Hitler acted in support of Zionism, along with his constant repetition of that distortion, has been a repulsive spectacle.
“We felt sure that the Labour Party, blighted by anti-Semitism as it is, would reclaim some of its former self and expel him. Labour has long had a moral duty to expel Ken Livingstone, but instead it has allowed his vile views to gain support in the party.”